mathematics-class-11-unit-11-chapter-3-straight-lines-l-3-6-3aqgiek3sj0

<p><Success style="float:center;text-align:center;font-size:22px;" ><B>Straight line Lecture 3</B></Success></p>
<p><Primary style="float:center;text-align:center;font-size:24px;"><B>Example 2</B></Primary></p>
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<p>Find the equation of the line passing through $(2,3)$ and making equal intercepts on the coordinate axes.</p>
<p><strong>Solution:</strong></p>
<p>Let intercepts are $a$ & $a$</p>
<p>$\frac{x}{a}+\frac{y}{a}= 1$</p>
<p>$\Rightarrow x + y = a\rightarrow l$</p>
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Reduction of general form Ax+By+c=0 to other forms$\to$1. Reduction to slope - intercept form$\to$Reduction to intercept form$\to$Reduction to normal form$\to$<span style="color:blue">Example</span>$\to$Solution
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<p>======</p>
<p><Success style="float:center;text-align:center;font-size:22px;" ><B>Straight line Lecture 3</B></Success></p>
<p><Primary style="float:center;text-align:center;font-size:24px;"><B>Example 2</B></Primary></p>
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<p>line l passing through $(2,3)$</p>
<p>$2 + 3 =a \Rightarrow a=5$</p>
<p>$\frac{x}{5} + \frac{y}{5} =1 \Rightarrow 2 + y = 5$</p>
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<footer style='font-size:18px'>
Reduction of general form Ax+By+c=0 to other forms$\to$1. Reduction to slope - intercept form$\to$Reduction to intercept form$\to$Reduction to normal form$\to$<span style="color:blue">Example</span>$\to$Solution
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<p><Success style="float:center;text-align:center;font-size:22px;" ><B>Straight line Lecture 3</B></Success></p>
<p><Primary style="float:center;text-align:center;font-size:24px;"><B>Example 7</B></Primary></p>
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<p>Find the equation of the stright line which passing through the point (-1,3) and is perpendicular to the line $4x+3y+1=0.$</p>
<p><strong>Solution:</strong></p>
<p>Given equation of line $l_1: 4x+3y+1=0$</p>
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<hr>
<footer style='font-size:18px'>
Reduction of general form Ax+By+c=0 to other forms$\to$1. Reduction to slope - intercept form$\to$Reduction to intercept form$\to$Reduction to normal form$\to$<span style="color:blue">Example</span>$\to$Solution
</footer>
<p>======</p>
<p><Success style="float:center;text-align:center;font-size:22px;" ><B>Straight line Lecture 3</B></Success></p>
<p><Primary style="float:center;text-align:center;font-size:24px;"><B>Solution</B></Primary></p>
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<p>$\therefore$ slope of $l_1(m_1)=-\frac{4}{3}$</p>
<p>Since $ l_1 \text{ perpendiculer } l_2 $</p>
<p>$ m_1 \times m_2= -1 $</p>
<p>$m_2=-\frac{1}{m_1}=\frac{3}{4}$</p>
<p>Equation of line $l_1$ passing through $l(-1,3)$ is</p>
<p>$(y-3) =\frac{3}{4} (x+1)$</p>
<p>$\Rightarrow 4y-12 = 3x + 3 \Rightarrow 3x-4y + 15=0$</p>
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<hr>
<footer style='font-size:18px'>
Reduction of general form Ax+By+c=0 to other forms$\to$1. Reduction to slope - intercept form$\to$Reduction to intercept form$\to$Reduction to normal form$\to$Example$\to$<span style="color:blue">Solution</span>
</footer>

<p><Success style="float:center;text-align:center;font-size:22px;" ><B>Straight line Lecture 3</B></Success></p>
<p><Primary style="float:center;text-align:center;font-size:24px;"><B>Example 9</B></Primary></p>
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<p>By using the concept of equation of a line, that three points $(3,0), (-2,-2)$ and $(8,2)$ are collinear.</p>
<p><strong>Solution:</strong></p>
<p>Given three points $A(3,0), B(-2,-2)$ and $C(8,2)$</p>
<p>Equation of $AB, (y-0) = \frac{0+2}{3+2} (x-3)$</p>
<p>$\Rightarrow y=\frac{2}{5} (x-3)$</p>
<p>$\Rightarrow 5y = 2x-6 \Rightarrow 2x-5y-6=0$</p>
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<hr>
<footer style='font-size:18px'>
Reduction of general form Ax+By+c=0 to other forms$\to$1. Reduction to slope - intercept form$\to$Reduction to intercept form$\to$Reduction to normal form$\to$<span style="color:blue">Example</span>$\to$Solution
</footer>
<p>======</p>
<p><Success style="float:center;text-align:center;font-size:22px;" ><B>Straight line Lecture 3</B></Success></p>
<p><Primary style="float:center;text-align:center;font-size:24px;"><B>Solution</B></Primary></p>
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<p>put $x = 8$ & $y = 2$ in the equation of line</p>
<p>$2 \times 8 - 5 \times 2 - 6= 16-16=0$</p>
<p>$\therefore$ Hence C(8,2) satisfied the $Q \leqq$</p>
<p>$\therefore$ C(8,2) lies on the line.</p>
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<p><img alt="image" src="http://115.241.75.180/iitpal-images/m11/mathematics-class-11-unit-11-chapter-3-straight-lines-l-3_6-3aqgiek3sj0/img/215-2443.2.jpg"></p>
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<hr>
<footer style='font-size:18px'>
Reduction of general form Ax+By+c=0 to other forms$\to$1. Reduction to slope - intercept form$\to$Reduction to intercept form$\to$Reduction to normal form$\to$Example$\to$<span style="color:blue">Solution</span>
</footer>